Existence and Ulam-Hyers stability results for multivalued coincidence problems

Abstract

In this paper, we will present some existence and Ulam-Hyers stability results for fixed point and coincidence point problems with multivalued operators using the weakly Picard operator technique in spaces endowed with vector metrics.

Bounds for solutions of linear differential equations and Ulam stability

“…So, generally we say that equation (1.1) is stable (or generalized stable) in Ulam sense if for every approximate solution of the equation there exists an exact solution close to it. For more details on Ulam stability see [2][3][4]8].…”

On coupled best proximity points and Ulam–Hyers stability

“…Let A and B be nonempty subsets of a normed linear space X. A mapping T : A → B is a cyclic nonexpansive mapping if it satisfies the following conditions: Recently, many authors (see [5,8,9,11]) have studied Ulam-Hyers stability for integral equations, differential equations, operatorial equations and various fixed point problems in different spaces. In this paper we extend the notion of Ulam-Hyers stability to coupled best proximity point problem as follows:…”

“…Recently, many authors (see [5,8,9,11]) have studied Ulam-Hyers stability for integral equations, differential equations, operatorial equations and various fixed point problems in different spaces. In this paper we extend the notion of Ulam-Hyers stability to coupled best proximity point problem as follows:…”

A note on the Hyers-Ulam stability constants of closed linear operators

“…Due to the question of Ulam and the answer of Hyers the stability of equations is called after their names. Later, a large number of papers and books have been published in connection with various generalizations of Hyers-Ulam theorem [5,7,10,13,15,17]. For instance, S.-E. Takahasi, H. Takagi, T. Miura and S. Miyajima [15] investigated the Hyers-Ulam stability constant K T h of linear differential operator (T h u)(t) = u (t) + h(t)u(t) and pointed out that it would be interesting to investigate the properties of the mapping h → K T h .…”